While learning from climate statistics accumulated in time presents opportunities, it also comes with challenges. Accumulating statistics in time is computationally much more expensive than the forecasts over hours or days used in NWP. Therefore, we need algorithms for learning from data that minimize the number of climate model runs required. Traditional methods for Bayesian calibration and uncertainty quantification such as Markov chain Monte Carlo (MCMC) typically require many iterations—often more than \(10^5\) —to reach statistical convergence e.g., [1]}. Conducting so many computationally expensive climate model runs is not feasible, rendering MCMC impractical for climate model calibration [2]}. Additionally, while MCMC can be used to obtain the distribution of model parameters given data, it is not robust with respect to noise in the evaluation of the map from model parameters to data. Such noise, arising from natural variability in the chaotic climate system, can lead to trapping of the Markov chains in spurious, noise-induced local maxima of the likelihood function [3]}. This presents additional challenges to using MCMC methods for climate model calibration.
